What is the correct way to smooth sharp edges between faces?
You can go to vertex selection mode.

Select all the vertices.
Got to mesh option on the top.
Clean up &gt; merge by distance.
This will delete the unwanted vertcies.
If this does not work, you  should go to face select mode and apply correct normals ( shortcut : ctrl+ N, in edit mode obviously.

If you see any red color that means some thing is wrong. You need recalculate normals. If every thing you see from out side is blue then you are good to go.
Againg if it does not work just apply your mirror modifier on object mode and then give it a subdivision surface modifier then smoth shading.
Hope it helps.!